Graph forms
for C4 [ 168, 29 ] = KE_42(1,17,14,3,13)
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On this page are computer-accessible forms for the graph C4[ 168, 29 ] =
KE_42(1,17,14,3,13).
(I) Following is a form readable by MAGMA:
g:=Graph<168|{ {2, 3}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {4, 5}, {6, 7},
{8, 9}, {10, 11}, {12, 13}, {14, 15}, {16, 17}, {18, 19}, {20, 21}, {22, 23},
{24, 25}, {26, 27}, {28, 29}, {30, 31}, {32, 33}, {1, 2}, {41, 42}, {37, 38},
{5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22}, {25, 26}, {29, 30}, {33, 34}, {3,
4}, {35, 36}, {11, 12}, {19, 20}, {27, 28}, {128, 141}, {146, 159}, {144, 157},
{130, 143}, {80, 94}, {81, 95}, {7, 8}, {145, 158}, {39, 40}, {23, 24}, {129,
142}, {71, 85}, {74, 88}, {75, 89}, {78, 92}, {79, 93}, {131, 144}, {143, 156},
{139, 152}, {135, 148}, {132, 145}, {142, 155}, {140, 153}, {134, 147}, {76,
90}, {77, 91}, {133, 146}, {141, 154}, {32, 57}, {38, 63}, {36, 61}, {34, 59},
{33, 58}, {37, 62}, {128, 157}, {138, 151}, {130, 159}, {136, 149}, {72, 86},
{73, 87}, {15, 16}, {35, 60}, {129, 158}, {137, 150}, {131, 160}, {139, 168},
{135, 164}, {132, 161}, {134, 163}, {23, 48}, {31, 56}, {133, 162}, {24, 49},
{26, 51}, {28, 53}, {30, 55}, {64, 106}, {65, 107}, {68, 110}, {69, 111}, {80,
122}, {81, 123}, {84, 126}, {85, 127}, {1, 42}, {25, 50}, {29, 54}, {82, 127},
{138, 167}, {136, 165}, {66, 108}, {67, 109}, {82, 124}, {83, 125}, {27, 52},
{137, 166}, {82, 96}, {83, 97}, {147, 160}, {155, 168}, {151, 164}, {148, 161},
{150, 163}, {70, 112}, {71, 113}, {78, 120}, {79, 121}, {84, 98}, {149, 162},
{64, 120}, {65, 121}, {66, 122}, {67, 123}, {68, 124}, {69, 125}, {70, 126},
{18, 43}, {20, 45}, {22, 47}, {72, 114}, {73, 115}, {76, 118}, {77, 119}, {21,
46}, {152, 165}, {154, 167}, {74, 116}, {75, 117}, {19, 44}, {153, 166}, {31,
32}, {4, 71}, {8, 75}, {12, 79}, {16, 83}, {1, 68}, {3, 70}, {9, 76}, {11, 78},
{17, 84}, {2, 69}, {10, 77}, {43, 99}, {59, 115}, {58, 114}, {57, 113}, {56,
112}, {47, 103}, {46, 102}, {45, 101}, {44, 100}, {60, 116}, {61, 117}, {62,
118}, {63, 119}, {5, 72}, {7, 74}, {6, 73}, {1, 85}, {42, 126}, {41, 125}, {40,
124}, {35, 119}, {34, 118}, {2, 86}, {3, 87}, {8, 92}, {9, 93}, {10, 94}, {11,
95}, {32, 116}, {33, 117}, {54, 96}, {55, 97}, {62, 104}, {63, 105}, {48, 104},
{55, 111}, {54, 110}, {53, 109}, {52, 108}, {51, 107}, {50, 106}, {49, 105},
{56, 98}, {57, 99}, {60, 102}, {61, 103}, {4, 88}, {39, 123}, {38, 122}, {37,
121}, {36, 120}, {5, 89}, {6, 90}, {7, 91}, {13, 80}, {15, 82}, {58, 100}, {59,
101}, {14, 81}, {39, 64}, {40, 65}, {42, 67}, {48, 90}, {53, 95}, {52, 94}, {49,
91}, {41, 66}, {12, 96}, {13, 97}, {14, 98}, {15, 99}, {28, 112}, {29, 113},
{30, 114}, {31, 115}, {50, 92}, {51, 93}, {16, 100}, {17, 101}, {18, 102}, {19,
103}, {24, 108}, {25, 109}, {26, 110}, {27, 111}, {46, 88}, {47, 89}, {44, 86},
{45, 87}, {20, 104}, {21, 105}, {22, 106}, {23, 107}, {43, 85}, {43, 130}, {57,
144}, {47, 134}, {45, 132}, {59, 146}, {61, 148}, {63, 150}, {46, 133}, {58,
145}, {62, 149}, {44, 131}, {60, 147}, {48, 135}, {56, 143}, {49, 136}, {55,
142}, {53, 140}, {51, 138}, {50, 137}, {54, 141}, {52, 139}, {83, 128}, {84,
129}, {86, 128}, {87, 129}, {94, 136}, {95, 137}, {118, 160}, {119, 161}, {126,
168}, {64, 151}, {72, 159}, {65, 152}, {67, 154}, {69, 156}, {71, 158}, {88,
130}, {89, 131}, {92, 134}, {93, 135}, {120, 162}, {121, 163}, {124, 166}, {125,
167}, {66, 153}, {70, 157}, {90, 132}, {91, 133}, {122, 164}, {123, 165}, {68,
155}, {127, 156}, {73, 160}, {75, 162}, {77, 164}, {79, 166}, {96, 138}, {97,
139}, {100, 142}, {101, 143}, {112, 154}, {113, 155}, {116, 158}, {117, 159},
{74, 161}, {78, 165}, {98, 140}, {99, 141}, {114, 156}, {115, 157}, {76, 163},
{127, 140}, {102, 144}, {103, 145}, {110, 152}, {111, 153}, {80, 167}, {81,
168}, {104, 146}, {105, 147}, {108, 150}, {109, 151}, {106, 148}, {107, 149}
}>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 85)(3, 71)(5, 88)(6, 74)(8, 91)(9, 77)(11, 94)(12, 80)(14, 97)(15,
83)(17, 100)(18, 44)(20, 103)(21, 47)(23, 106)(24, 50)(26, 109)(27, 53)(29,
112)(30, 56)(32, 115)(33, 59)(35, 118)(36, 62)(38, 121)(39, 65)(41, 124)(42,
68)(43, 86)(45, 145)(46, 89)(48, 148)(49, 92)(51, 151)(52, 95)(54, 154)(55,
98)(57, 157)(58, 101)(60, 160)(61, 104)(63, 163)(64, 107)(66, 166)(67, 110)(69,
127)(70, 113)(72, 130)(73, 116)(75, 133)(76, 119)(78, 136)(79, 122)(81, 139)(82,
125)(84, 142)(87, 158)(90, 161)(93, 164)(96, 167)(99, 128)(102, 131)(105,
134)(108, 137)(111, 140)(114, 143)(117, 146)(120, 149)(123, 152)(126, 155) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (2, 42)(3, 41)(4, 40)(5, 39)(6, 38)(7, 37)(8, 36)(9, 35)(10, 34)(11, 33)(12,
32)(13, 31)(14, 30)(15, 29)(16, 28)(17, 27)(18, 26)(19, 25)(20, 24)(21, 23)(43,
110)(44, 109)(45, 108)(46, 107)(47, 106)(48, 105)(49, 104)(50, 103)(51, 102)(52,
101)(53, 100)(54, 99)(55, 98)(56, 97)(57, 96)(58, 95)(59, 94)(60, 93)(61,
92)(62, 91)(63, 90)(64, 89)(65, 88)(66, 87)(67, 86)(68, 85)(69, 126)(70,
125)(71, 124)(72, 123)(73, 122)(74, 121)(75, 120)(76, 119)(77, 118)(78, 117)(79,
116)(80, 115)(81, 114)(82, 113)(83, 112)(84, 111)(127, 155)(128, 154)(129,
153)(130, 152)(131, 151)(132, 150)(133, 149)(134, 148)(135, 147)(136, 146)(137,
145)(138, 144)(139, 143)(140, 142)(156, 168)(157, 167)(158, 166)(159, 165)(160,
164)(161, 163)
c: (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42)(43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61,
62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
82, 83, 84)(85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100,
101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116,
117, 118, 119, 120, 121, 122, 123, 124, 125, 126)(127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148,
149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
165, 166, 167, 168)
C4[ 168, 29 ]
168
-1 2 68 85 42
-2 1 3 69 86
-3 2 4 70 87
-4 88 3 5 71
-5 89 4 6 72
-6 90 5 7 73
-7 91 6 8 74
-8 92 7 9 75
-9 93 8 10 76
-10 11 77 94 9
-11 12 78 95 10
-12 11 13 79 96
-13 12 14 80 97
-14 13 15 81 98
-15 99 14 16 82
-16 100 15 17 83
-17 101 16 18 84
-18 102 17 19 43
-19 44 103 18 20
-20 45 104 19 21
-21 22 46 105 20
-22 23 47 106 21
-23 22 24 48 107
-24 23 25 49 108
-25 24 26 50 109
-26 110 25 27 51
-27 111 26 28 52
-28 112 27 29 53
-29 113 28 30 54
-30 55 114 29 31
-31 56 115 30 32
-32 33 57 116 31
-33 34 58 117 32
-34 33 35 59 118
-35 34 36 60 119
-36 35 37 61 120
-37 121 36 38 62
-38 122 37 39 63
-39 123 38 40 64
-40 124 39 41 65
-41 66 125 40 42
-42 1 67 126 41
-43 99 18 85 130
-44 100 19 86 131
-45 132 101 20 87
-46 88 133 102 21
-47 22 89 134 103
-48 23 90 135 104
-49 24 91 136 105
-50 25 92 137 106
-51 26 93 138 107
-52 27 94 139 108
-53 28 95 140 109
-54 110 29 96 141
-55 111 30 97 142
-56 143 112 31 98
-57 99 144 113 32
-58 33 100 145 114
-59 34 101 146 115
-60 35 102 147 116
-61 36 103 148 117
-62 37 104 149 118
-63 38 105 150 119
-64 39 106 151 120
-65 121 40 107 152
-66 122 41 108 153
-67 154 123 42 109
-68 110 1 155 124
-69 111 2 156 125
-70 112 3 157 126
-71 113 4 158 85
-72 114 5 159 86
-73 115 6 160 87
-74 88 116 7 161
-75 89 117 8 162
-76 90 118 9 163
-77 91 119 10 164
-78 11 165 92 120
-79 121 12 166 93
-80 122 13 167 94
-81 123 14 168 95
-82 124 15 127 96
-83 125 16 128 97
-84 126 17 129 98
-85 1 71 127 43
-86 44 2 72 128
-87 45 3 73 129
-88 46 4 74 130
-89 47 5 75 131
-90 132 48 6 76
-91 77 133 49 7
-92 78 134 50 8
-93 79 135 51 9
-94 80 136 52 10
-95 11 81 137 53
-96 12 82 138 54
-97 55 13 83 139
-98 56 14 84 140
-99 57 15 141 43
-100 44 58 16 142
-101 143 45 59 17
-102 144 46 60 18
-103 145 47 61 19
-104 146 48 62 20
-105 147 49 63 21
-106 22 148 50 64
-107 23 149 51 65
-108 66 24 150 52
-109 67 25 151 53
-110 68 26 152 54
-111 55 69 27 153
-112 154 56 70 28
-113 155 57 71 29
-114 156 58 72 30
-115 157 59 73 31
-116 158 60 74 32
-117 33 159 61 75
-118 34 160 62 76
-119 77 35 161 63
-120 78 36 162 64
-121 79 37 163 65
-122 66 80 38 164
-123 165 67 81 39
-124 166 68 82 40
-125 167 69 83 41
-126 168 70 84 42
-127 156 82 85 140
-128 157 83 86 141
-129 158 84 87 142
-130 88 143 159 43
-131 44 89 144 160
-132 45 90 145 161
-133 46 91 146 162
-134 47 92 147 163
-135 48 93 148 164
-136 165 49 94 149
-137 166 50 95 150
-138 167 51 96 151
-139 168 52 97 152
-140 127 53 98 153
-141 99 154 128 54
-142 55 100 155 129
-143 56 101 156 130
-144 57 102 157 131
-145 132 58 103 158
-146 133 59 104 159
-147 134 60 105 160
-148 135 61 106 161
-149 136 62 107 162
-150 137 63 108 163
-151 138 64 109 164
-152 110 165 139 65
-153 66 111 166 140
-154 67 112 167 141
-155 68 113 168 142
-156 143 69 114 127
-157 144 70 115 128
-158 145 71 116 129
-159 146 72 117 130
-160 147 73 118 131
-161 132 148 74 119
-162 133 149 75 120
-163 121 134 150 76
-164 77 122 135 151
-165 78 123 136 152
-166 79 124 137 153
-167 154 80 125 138
-168 155 81 126 139
0